| Most current applications and uses of liquid crystalline materials involve surfaces and interfaces. Prominent examples are high performance carbonaceous mesophase fibers, liquid crystal polymer fibers, and thermoplastic/liquid crystal polymer in-situ composites. Fundamental surface science and engineering principles are needed to optimize and design fibers and composites derived from liquid crystalline precursors. Currently non-equilibrium liquid crystal surface phenomena are not well understood. Force balance equations describing static and dynamical interfacial phenomena are available but have not been adequately used to describe the mechanics of fiber and film microstructures.; This thesis explores the mechanics and stability of nematic liquid crystalline fibers embedded in inviscid and viscous matrices. A new theoretical framework for liquid crystal surface mechanics is formulated and used to model pattern formation and instability driven processes in fibers and fibrillar composites and blends. The liquid crystal Herring's formula and Laplace equation are derived and the role of liquid crystallinity is elucidated. In order to systematically analyze the role of the fundamental processes, linear stability analyses of capillary instabilities in nematic liquid crystalline fibers are performed by formulating and solving the governing nemato-capillary equations. An essential characteristic of liquid crystals, in contrast to isotropic liquids, is their mechanical anisotropy. Thus, the main parameters affecting the capillary instabilities are the isotropic and anisotropic surface tensions, the anisotropic viscosities, the bulk orientational elasticity, the isotropic viscosity of the matrix, and the surface bending modulus. Two asymptotic regimes are investigated: (a) the thin-fiber regime characterized by homogeneous bulk orientation and storage of surface elasticity, and (b) the thick-fiber regime characterized by bulk orientation distortions without surface elastic storage. Novel capillary instability mechanisms and symmetries of the instability modes for a nematic fiber embedded in a matrix are characterized. The predicted ability of capillary instabilities in nematic fibers to produce surface structures of well-defined symmetry and length scales, as well as chiral microstructures, is an important result that augments the pathways for targeted pattern formation. Deviations from classical Rayleigh capillary instabilities are identified and quantified in terms of liquid crystalline order. |
